Conformal surface plasmons propagating on ultrathin and flexible films

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Conformal surface plasmons propagating on ultrathin and flexible films Xiaopeng Shena,1, Tie Jun Cuia,1,2, Diego Martin-Canob, and Francisco J. Garcia-Vidalb,c,2 a State Key Laboratory of Millimetre Waves, School of Information Science and Engineering, Southeast University, Nanjing 210096, China; bDepartamento de Fisica Teorica de la Materia Condensada, Universidad Autonoma de Madrid, E-28049 Madrid, Spain; and cDonostia International Physics Center, 20018 San Sebastian/Donostia, Spain

Edited† by Federico Capasso, Harvard University, Cambridge, MA, and approved November 15, 2012 (received for review June 18, 2012)

Surface plasmon polaritons (SPPs) are localized surface electromagnetic waves that propagate along the interface between a metal and a dielectric. Owing to their inherent subwavelength confinement, SPPs have a strong potential to become building blocks of a type of photonic circuitry built up on 2D metal surfaces; however, SPPs are difficult to control on curved surfaces conformably and flexibly to produce advanced functional devices. Here we propose the concept of conformal surface plasmons (CSPs), surface plasmon waves that can propagate on ultrathin and flexible films to long distances in a wide broadband range from microwave to mid-infrared frequencies. We present the experimental realization of these CSPs in the microwave regime on paper-like dielectric films with a thickness 600-fold smaller than the operating wavelength. The flexible paper-like films can be bent, folded, and even twisted to mold the flow of CSPs. metamaterials

| plasmonics | waveguiding

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urface plasmon polaritons (SPPs) are highly localized surface waves (1) that propagate along the interface between two materials whose real parts of electric permittivity have opposite signs, and decay exponentially in the transverse direction. At optical frequencies, metals behave like plasma with negative permittivity, and thus SPPs exist on metal–air interfaces (2, 3). Owing to their ability to confine light in a subwavelength scale with high intensity, SPPs can be used to overcome the diffraction limit, miniaturize photonic components, and build highly integrated optical components and circuits. Thus, they have found (or have potential) applications in biomedical sensing, near-field microscopy, optoelectronics, photovoltaics, and nanophotonics (4–11). In the far-infrared, terahertz, and microwave frequency bands, metals behave akin to perfectly electrical conductors (PECs), and thus SPPs cannot be supported by a metal surface. Although some designs based on metal wires or strips are able to support surface leaky modes that have some degree of lateral confinement at terahertz frequencies (12, 13), the concept of plasmonic metamaterials has proven very useful in the production of highly confined surface electromagnetic (EM) waves at low frequencies (14– 27). Early work in this area can be traced back to the 1950s and 1960s, when corrugated metal structures were used to generate surface EM waves at microwave frequencies (14, 15). Generally, plasmonic metamaterials consist of metal surfaces decorated with 1D arrays of subwavelength grooves, 2D arrays of subwavelength holes/dimples, or 3D metal wires in which a periodic array of radial grooves is drilled (16–26). Recently, an alternative “spoof” SPP structure using complementary split-ring resonators as the unit cell elements has been proposed theoretically (27). The surface EM modes decorated by all of these plasmonic metamaterials are called spoof SPPs, or designer SPPs, because their properties are very similar to those of SPPs at optical frequencies. An important advantage of this metamaterial approach is that the dispersion characteristics and spatial confinement of the spoof SPPs can be controlled simply by geometrical means. However, all of the aforementioned plasmonic metamaterials have a major limitation associated with their inherent 3D geometry. 40–45 | PNAS | January 2, 2013 | vol. 110 | no. 1

For the production of advanced plasmonic functional devices, it is very important to realize surface EM waves that can be confined in the subwavelength scale and can propagate on flexible and curved surfaces. Electronic and photonic circuits, devices, and systems integrated on flexible, stretchable, and biocompatible curved substrates have numerous applications, including electronic eyeball cameras (28), personal health monitors and biomedical devices (29), deformable light-emitting displays (30), adaptive photonic systems (31), human body sensors (32), paperlike electronic displays (33), artificial skin sensors (34), and electronic vivo brain monitoring devices (35). More recently, nanoscale stencils fabricated on flexible and stretchable substrate have been used as plasmonic nanoantennas at infrared frequencies (36). Because flexible and stretchable photonic structures can be wrapped on curved surfaces and objects, they have advantages over devices integrated on traditional rigid wafer-based substrates. For both SPPs and spoof SPPs, much of the research to date has concentrated on flat surfaces: SPPs on flat metal surfaces and spoof SPPs on flat virtual surfaces (i.e., flat metal surfaces plus periodic arrays of grooves or pits). At optical frequencies, it is difficult to make SPPs travel for long distances on curved metal surfaces because of radiation losses, particularly when the curvature radius is on the order of the SPP wavelength. At terahertz and microwave frequencies, it is even more difficult to make spoof SPPs propagate along curved surfaces, owing to the 3D character of the plasmonic metamaterials used up to now. Thus, the propagation of either SPPs or spoof SPPs on curved surfaces has not yet been realized. Results and Discussions In this work, we propose the concept of conformal surface plasmons (CSPs), a type of surface EM wave that is supported by ultrathin films and whose propagation adapts to the curvature of the surface. These CSP modes are realized using nearly zero-thickness metal strips printed on flexible, ultrathin dielectric films. Our proposed plasmonic metamaterial that supports CSPs has a comb shape (Fig. 1A, Inset) and consists of a metal strip of thickness t and width W, in which a 1D periodic array of grooves of depth h is drilled. The period of the array is d, and the width of the groove is a. When the thickness t approaches infinity, the structure reduces to a 1D array of grooves (19). We analyzed the evolution of the dispersion relation of the surface EM waves supported by this structure with thickness t (Fig. 1A). We assumed that the metal behaves as a PEC, and thus that the results are scalable simply by modifying d, which

Author contributions: T.J.C. and F.J.G.-V. designed research; X.S., T.J.C., D.M.-C., and F.J.G.-V. performed research; X.S., T.J.C., D.M.-C., and F.J.G.-V. analyzed data; and X.S., T.J.C., D.M.-C., and F.J.G.-V. wrote the paper. The authors declare no conflict of interest. †

This Direct Submission article had a prearranged editor.

Freely available online through the PNAS open access option. 1

X.S. and T.J.C. contributed equally to this work.

2

To whom correspondence may be addressed. E-mail: [email protected] or [email protected].

This article contains supporting information at www.pnas.org/lookup/suppl/doi:10.1073/ pnas.1210417110/-/DCSupplemental.

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is treated as the unit of length in our calculations. We used a finite element method (FEM) implemented in COMSOL Multiphysics to numerically calculate the dispersion curves of the TM-polarized waves propagating along the z-direction with momentum k. All of the bands for different thicknesses (ranging from infinity to 0.002d) deviated significantly from the light line (gray curve in Fig. 1A), indicating that the corrugated metal plate supports the propagation of confined modes. The dispersion curves exhibited SPP-like behavior, presenting an asymptote controlled mainly by h and t. In contrast to the SPP modes at optical frequencies, in which this surface EM wave is built up as the result of the hybridization of a grazing photon with the collective plasma oscillations of the electrons, here the resonant mode of the cavities couples with the grazing photon. For a 1D array of grooves (infinite t), the initial πc , which then dictates the cavity mode appears at frequency ωc = 2h asymptote frequency of the corresponding surface EM mode. For this case, the electric field (E-field) points along the z-direction within the grooves, whereas the magnetic field (H-field) is directed along the x-direction. The important point to note is that when t is decreased to a finite value, the two cavity sides parallel to the yz plane are open, and thus the H-field remains unquantized in the xdirection. That is why the dispersion relation of the surface EM mode is insensitive to the thickness of the metal, in much the same way as domino plasmons (23, 37). Accordingly, there remains a surface EM mode supported by the structure in the limit of zero thickness. Because the dispersion relation of the mode remains unaltered, the subwavelength nature of its confinement is maintained when going from very large t to a nearly zero-thickness comb-shaped strip. Shen et al.

An important question concerns the frequency regimes in which these surface EM waves can operate. Fig. 1B shows the dispersion curves of the propagating EM modes for the same geometric parameters as in Fig. 1A with t = 0.02d but different values of d, ranging from 5 mm (to operate in the microwave regime) to 5 μm (to operate in the mid-infrared regime). To calculate these bands, in our numerical simulations we introduced the actual dielectric function of metal (copper in this case), as tabulated previously (38). The primary point to note is that the dispersion curves (d/λ) are not very sensitive to the frequency regime of operation, demonstrating that CSPs exist at microwave, terahertz, and mid-infrared frequencies. As expected, the corresponding propagation lengths (Fig. 1B, Inset) are much more sensitive to the frequency regime, because ohmic losses in the metal become more important with increasing frequency. Nevertheless, it is noteworthy that the propagation length of these CSP modes can be greatly enhanced through properly designed geometric parameters. Simply reducing h and/or increasing W will increase CSP propagation lengths by one order of magnitude compared with those shown in Fig. 1B, Inset. CSPs are also supported by symmetric comb structures in which the two sides of the planar metal strip are symmetrically corrugated by two 1D arrays of grooves. Hybridization of the two CSP modes associated with these two combs leads to the emergence of two surface EM modes, as illustrated by their dispersion relations in Fig. 1A (dashed lines). As expected, this symmetrical combination leads to a confined mode with a lower frequency than that of the CSP mode of a single comb-shaped structure, whereas the antisymmetric mode is spectrally located at higher frequencies, closer to the light line. Owing to its higher confinement, the symmetric mode has a shorter propagation length (80λ for λ = d, with PNAS | January 2, 2013 | vol. 110 | no. 1 | 41

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Fig. 1. Dispersion relationships and local field distributions of the comb-shaped CSP structures. (A) Normalized dispersion relations for the fundamental CSP mode as a function of thickness, t. (Inset) Geometric parameters of the structure, with W = d, a = 0.4d, and h = 0.8d fixed for all curves. The metal is modeled as a PEC. Continuous lines render the dispersion relations of single comb-shaped structures for different values of t, whereas the two dashed lines correspond to a double comb-shaped structure with t = 0.02d. (B) Variation of the dispersion relation with different values of d using copper optical constants and the same geometric parameters as in A for t = 0.02d. The PEC curve from A is also displayed for comparison purposes. (Inset) Propagation lengths normalized to the operating wavelength for the same values of d as in the main panel. (C) Amplitude (modulus) of the electric field evaluated at the yz plane that cuts the metal symmetrically, with the color scale ranging from red (highest amplitude) to dark blue (lowest amplitude). The white arrows depict the yz components of the electric field, showing its phase variation along the propagation direction. (D) Power flow contour plots evaluated at two transverse xy planes cutting the grooves (Left) and teeth (Right) of the comb-shaped structure. The color scale ranges from red (highest intensity) to dark blue (lowest intensity), and the white arrows depict the xy components of the magnetic field. The orange line denotes the modal size of the CSP mode, which represents 70% of the integrated energy flow. All geometric parameters in C and D correspond to those in B, with d = 5 mm and an operating wavelength of 30 mm.

d = 5 mm) compared with its single comb counterpart (115λ for λ = d, with d = 5 mm) (Fig. 1B, Inset). However, on a positive note, it is much less sensitive to bending losses, which could be important when designing curved waveguides. The antisymmetric mode demonstrates the opposite behavior; although it is a very longranging CSP mode (propagation length, 440λ for λ = d, with d = 5 mm), its radiative losses are very large in curved geometries. Although symmetric comb structures could have some advantages over asymmetric comb structures in terms of smaller bending losses, single comb-shaped structures are superior because they are singlemode waveguides. For this reason, in what follows we concentrate on analyzing and testing the properties of asymmetric structures. A key characteristic of the CSP modes is that they are confined at a very deep subwavelength scale in the three spatial dimensions. This property is illustrated in Fig. 1 C and D, which shows the Efield (vector field in white arrows and field amplitude in color scale) evaluated in a yz plane just above the structure (C) and the H vector field (white arrows) and flux intensity (color scale) calculated in two xy planes within the unit cell (D). In the latter panel, the closed orange curve denotes the area in which 70% of the flux energy of the propagating mode is contained. The EM field is highly localized within the comb-shaped metal structure, which has important implications for control in the propagation of CSP modes. The dispersion relations and local fields shown in Fig. 1 demonstrate that the surface EM waves on corrugated ultrathin metal strips exhibit SPP-like behavior. This is further confirmed by an analysis of their field confinement and propagation lengths (see below). As discussed earlier, the characteristics of CSP propagation can be controlled by adjusting the strip width W and/or the groove depth h. By fixing W = d, a = 0.4d, and t = 0.0036d (with d = 5 mm as the periodicity), we now consider two ultrathin corrugated metal strips with different groove depths (h = 0.8d and h = 0.7d). From the dispersion relations (Fig. S1), we observe a decrease in asymptote frequency and an increase in deviation of the dispersion curve with respect of the light line as the groove depth increases. This implies a stronger field confinement, which is confirmed by full-wave numerical simulations. In the calculations that follow, we use the commercial software CST Microwave Studio. We set the boundary conditions as “open” to simulate the real space, and set the boundaries at large distances from the metal structure to avoid spurious reflections. Fig. 2 A and B illustrates the simulated electric fields (Ez components) evaluated at the top of two strips (16λ long, with λ as the wavelength) with different corrugations at 12 GHz. An electric monopole pointing to the y direction with unity current is used for excitation at the left edge. We see that the surface EM waves are tightly confined and propagate along the straight waveguide with very small losses. The confinement details can be clearly seen from the distributions of electric field amplitudes (jEj = [jExj2+jEyj2+jEzj2]1/2) in the cross-sections perpendicular to the strips (dashed line in Fig. 2 A and B), as illustrated in Fig. 2 C and D. We note that the deeper corrugated metal strip confines the CSP mode to a smaller region with more significant field enhancement (Fig. 2D). For quantitative descriptions, Fig. 2 E and F shows the field distributions along two lateral cuts (the white dashed lines in Fig. 2 C and D). Both fields clearly decay exponentially along the two orthogonally lateral (y and z) directions (although they are asymmetrical along the strip direction, owing to their geometric asymmetry), illustrating the typical features of SPP modes. As the groove depth h increases, confinement tightens and field enhancement increases, whereas propagation length diminishes. FEM calculations show that the propagation length of the CSP mode is significantly reduced with increasing h; for h = 0.7d, this length is 100 times the wavelength, compared with 67 times the wavelength for h = 0.8d. This trade-off is characteristic of CSP modes between localization and propagation loss, the same as for standard SPPs at optical frequencies. 42 | www.pnas.org/cgi/doi/10.1073/pnas.1210417110

Fig. 2. Propagation of surface EM waves and field confinements on two ultrathin corrugated metal strips (W = d, t = 0.0036d, a = 0.4d, and d = 5 mm) with different groove depths (h = 0.8d and h = 0.7d). The operating frequency is 12 GHz (λ = 25 mm). An electric monopole pointing to the y direction with unit current is used for excitation at the left edge. (A and B) Simulated amplitudes of electric fields (jEj) on the two corrugated metal strips (A: h = 0.8d; B: h = 0.7d) over a length of 400 mm (16λ). (C and D) Field distributions on the cross-sections of the two corrugated metal strips (C: h = 0.8d; D: h = 0.7d) located 300 mm (12λ) away from the source (the dashed line in A and B). The black lines indicate the cross-sections of the two strips. The CSP modes are tightly confined to the corrugated strips with strong field enhancements. (E and F) Electric field distributions along the vertical cut (E) and horizontal cut (F), shown by the orthogonal dashed lines in C and D. The fields near the deeply corrugated strip (h = 0.8d) are much stronger and decay exponentially faster compared with those of the shallowly corrugated strip (h = 0.7d) along the two orthogonal directions.

To realize the CSPs experimentally, we performed a series of experiments in the microwave regime by constructing comb-shaped corrugated metal strips with d = 5 mm. The corresponding plasmonic metamaterials were manufactured using the standard printed circuit board fabrication process on a three-layer flexible copper-clad laminate (FCCL), consisting of a single layer of polyimide and an electrolytic copper-clad sheet connected with the epoxy adhesive. The thicknesses of polymide, adhesive, and copper foil layers were 12.5, 13, and 18 μm (t = 0.0036d), respectively, and thus the total film thickness was 43.5 μm. The fabricated samples are ultrathin and flexible (Fig. 3A). They can be wrapped around curved surfaces, and thus are well suited for incorporation into arbitrarily curved surfaces to mold the flow of CSPs. The highly localized features of these surface EM modes precludes their characterization by traditional far-field technologies; thus, we used a near-field scanning system to map the localized fields along the structured metal films (Fig. S2). The experimental setup consisted of an Agilent N5230C vector network analyzer and two monopole antennas as the source and detector. The detector, controlled by two computer-controlled step motors, was fixed at 1.5 mm above the samples and moved to scan the perpendicular component of the E-field (Fig. S2B). The scanning step was 1 mm, to obtain high-resolution pictures. E-field magnitude and phase data were collected and recorded by the network analyzer. We first conducted experiments on straightly planar structures with four different groove depths h and metal widths (h =3, 4, 5, and 6 mm and W = h+1 mm) and fixed a = 2 mm over flat, Shen et al.

300-mm-long FCCL strips (Fig. 3A). The operating frequency was fixed at 10 GHz. The full-wave simulation and measured electric fields (Ez components) for h =3 mm are shown in Fig. 3B, (i) and (ii), and other findings are shown in Fig. S3. These results demonstrate that the ultrathin comb-shaped metal strips can indeed confine surface EM waves in the lateral direction very efficiently while maintaining the intensities over distances much longer than the wavelength. To estimate the propagation loss of CSP modes quantitatively, we calculated the normalized timeaveraged power density (i.e., the Poynting vector, = 0.5Re [E×H*]) along an observation line lying 1.5 mm above the corrugated edge [Fig. 3B, (iii)]. For this particular set of geometric parameters, the propagation efficiency was as high as 98% after traveling over eight free-space wavelengths. Our second set of experiments and numerical simulations tested how the propagation of CSP modes is affected by the presence of bends or splitters that imply a change of direction in the plane, with the groove depth fixed at h = 4 mm. Fig. 3 C and D shows numerically (C) and experimentally (D) that the CSP modes experienced little radiation loss after propagation through a 90° bend. Here the radius of curvature was equal to the operating wavelength of 30 mm. Fig. 3C, Inset shows the time-averaged power density along a bending observation line that is always 1.5 mm above the bending corrugated edge, showing a radiation loss of